LeetCode 235. Lowest Common Ancestor of a Binary Search Tree

Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST.

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined
between two nodes v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).”

_______6______
/              \
___2__          ___8__
/      \        /      \
0      _4       7       9
/  \
3   5

For example, the lowest common ancestor (LCA) of nodes

2

and

8

is

6

.
Another example is LCA of nodes

2

and

4

is

2

,
since a node can be a descendant of itself according to the LCA definition.
分析：二叉排序树（又叫二叉查找树）或者是一棵空树，或者是具有下列性质的二叉树：

（1）若左子树不空，则左子树上所有结点的值均小于它的根结点的值；

（2）若右子树不空，则右子树上所有结点的值均大于它的根结点的值；

（3）左、右子树也分别为二叉排序树；

（4）没有键值相等的节点。(以上来自百度百科)
可以根据二叉排序树的特点，利用递归算法来解决：

代码：

/**
* Definition for a binary tree node.
* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode(int x) { val = x; }
* }
*/
public class Solution {
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
if(root == null || p == null || q == null) return null;
if(p.val < root.val && q.val < root.val){
return lowestCommonAncestor(root.left, p, q);
}
if(p.val > root.val && q.val > root.val){
return lowestCommonAncestor(root.right, p, q);
}
return root;
}
}